1+12+14+18+116+132+164+1128+1256+1512=
问题描述：
1+
+1 2
+1 4
+1 8
+1 16
+1 32
+1 64
+1 128
+1 256
=1 512
答
1+
+1 2
+1 4
+1 8
+1 16
+1 32
+1 64
+1 128
+1 256
1 512
=1+1-
+1 2
-1 2
+1 4
-1 4
+1 8
-1 8
+…+1 16
-1 128
+1 256
-1 256
1 512
=2-
1 512
=1
511 512
答案解析：根据数字特点，前一个分数都是后一个分数的2倍，因此可把每个分数拆成两个分数相减的形式，然后通过加减相互抵消，求得结果．
考试点：分数的巧算．
知识点：此题采用了裂项消项法，先进行分数裂项，然后通过加减相互抵消，求出结果．